fractional selectivity

in catalysis
The term @S05563@ (\(S\)) is used to describe the relative rates of two or more competing reactions on a @C00876@. Such @C01198@ includes cases of different reactants undergoing @S05680@ or of a single reactant taking part in two or more reactions. For the latter case, \(S\) may be defined in two ways. The first of these defines a fractional @S05563@, \(S_{\text{F}}\), for each product by the equation \[S_{\text{F}}=\frac{\xi _{i}}{\sum \xi _{i}}\] The second defines relative selectivities, \(S_{\text{R}}\), for each pair of products by \[S_{\text{R}}=\frac{\xi _{i}}{\xi _{j}}\] In each case, \(\xi _{i}\) and \(\xi _{j}\) are the rates of increase of the @E02283@ i and j respectively, i.e. \[\xi _{i}=\frac{\mathrm{d}\xi _{i}}{\mathrm{d}t}\] and \[\xi _{j}=\frac{\mathrm{d}\xi _{j}}{\mathrm{d}t}\] where \(\xi _{i}\) and \(\xi _{j}\) are the extents of reactions \(i\) and \(j\) respectively.
PAC, 1976, 46, 71. (Manual of Symbols and Terminology for Physicochemical Quantities and Units - Appendix II. Definitions, Terminology and Symbols in Colloid and Surface Chemistry. Part II: Heterogeneous Catalysis) on page 81 [Terms] [Paper]